firm trains operators to do certain tasks on a production line. Those operators

Question

firm trains operators to do certain tasks on a production line. Those operators wheo (6l end the training course are known to be able to meet their production quotas 90% of the time. Operators who do not take the training co time. Fifty percent of operators attend the course. (a) What is the probability that an operator meets her/his production quota? (b) Given that an operator meets his/her production quota, what is the probability t urse only meet their guotas 60% of the he/she attended the course? (6 points

Explanation / Answer

P(Trained operators meet quota) = .90

P(untrained operators meet quota) = .60

P(Training) = 0.5.

a)

P(Operator meets quota) = P(Training)* P(Trained operators meet quota) + P(no Training)* P(untrained operators meet quota)

= 0.5 * 0.90 + (1-0.5) * 0.60

= 0.45+0.30

= 0.75

b)

P(Training/Operator meets quota) =

P(Trained operators meet quota) / [P(Trained operators meet quota)+ P(unTrained operators meet quota)]

= 0.90 / (0.90+0.60)

= 0.90/1.5

= 0.60

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